Significant figures and scientific notations
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Significant Figures and Scientific Notations. Examples and Problems. Rules for Counting Significant Figures. 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. Leading zeroes precede all the nonzero digits and DO NOT count as

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Significant Figures and Scientific Notations

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Significant figures and scientific notations

Significant Figures and Scientific Notations

Examples and Problems


Significant figures and scientific notations

Rules for Counting Significant Figures

1. Nonzero integers always count as significant figures.

2. Zeros: There are three classes of zeroes.

  • Leading zeroes precede all the nonzero digits and DO NOT count as

  • significant figures. Example: 0.0025 has ____ significant figures.

  • Captive zeroes are zeroes between nonzero numbers. These always

  • count as significant figures. Example: 1.008 has ____ significant figures.

  • Trailing zeroes are zeroes at the right end of the number.

  • Trailing zeroes are only significant if the number contains a decimal point.

  • Example: 1.00 x 102 has ____ significant figures.

  • Trailing zeroes are not significant if the number does not contain a decimal

  • point. Example: 100 has ____ significant figure.

  • Exact numbers, which can arise from counting or definitions such as 1 in

  • = 2.54 cm, never limit the number of significant figures in a calculation.

2

4

3

1

Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination2006, page 53


Significant figures rules for zeros

Significant figures: Rules for zeros

Leading zeros are not significant.

Leading zero

– three significant figures

0.421

Captive zeros are significant.

Captive zero

4012

– four significant figures

Trailing zeros are significant.

Trailing zero

114.20

– five significant figures


Significant figures

Significant Figures

  • Counting Sig Figs

    • Count all numbers EXCEPT:

      • Leading zeros -- 0.0025

      • Trailing zeros without a decimal point -- 2,500

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


Significant figures1

3 SF

Significant Figures

  • Calculating with Sig Figs

    • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

4 SF

3 SF

324g

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


Significant figures2

Significant Figures

  • Calculating with Sig Figs (con’t)

    • Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

224 g

+ 130 g

354 g

224 g

+ 130 g

354 g

3.75 mL

+ 4.1 mL

7.85 mL

3.75 mL

+ 4.1 mL

7.85 mL

 350 g

 7.9 mL

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


Significant figures3

Significant Figures

  • Calculating with Sig Figs (con’t)

    • Exact Numbers do not limit the # of sig figs in the answer.

      • Counting numbers: 12 students

      • Exact conversions: 1 m = 100 cm

      • “1” in any conversion: 1 in = 2.54 cm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


Significant figures4

1. (15.30 g) ÷ (6.4 mL)

 2.4 g/mL

2 SF

Significant Figures

Practice Problems

4 SF

2 SF

= 2.390625 g/mL

2. 18.9g

- 0.84 g

 18.1 g

18.06 g

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


Scientific notation

Scientific Notation

65,000 kg  6.5 × 104 kg

  • Converting into scientific notation:

    • Move decimal until there’s 1 digit to its left. Places moved = exponent.

    • Large # (>1)  positive exponentSmall # (<1)  negative exponent

    • Only include sig. figs.

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


Scientific notation1

3. 2,400,000 g

4. 0.00256 kg

5. 7  10-5 km

6.6.2  104 mm

Scientific Notation

Practice Problems

2.4  106 g

2.56  10-3 kg

0.00007 km

62,000 mm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


Scientific notation2

EXE

EXP

EXP

ENTER

EE

EE

Scientific Notation

  • Calculating with scientific notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

Type on your calculator:

5.44

7

8.1

4

÷

= 671.6049383

= 670 g/mol

= 6.7 × 102 g/mol

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem


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